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Question Number 177475 by bekkiyor last updated on 05/Oct/22 Answered by a.lgnaoui last updated on 07/Oct/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 111939 by Khanacademy last updated on 05/Sep/20 Answered by bemath last updated on 05/Sep/20 $${consider}\:\mathrm{tan}\:{x}+\mathrm{tan}\:{y}\:=\:\mathrm{4} \\ $$$$\Rightarrow\:\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\:+\:\frac{\mathrm{sin}\:{y}}{\mathrm{cos}\:{y}}\:=\:\mathrm{4} \\ $$$$\Rightarrow\:\frac{\mathrm{sin}\:\left({x}+{y}\right)}{\mathrm{cos}\:{x}.\mathrm{cos}\:{y}}\:=\:\mathrm{4}\:\Rightarrow\:\mathrm{sin}\:\left({x}+{y}\right)=\mathrm{4}×\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\left({x}+{y}\right)\:=\:\mathrm{6}\:.\:{If}\:{x},{y}\in\mathbb{R}\:,\:{it}\:{is}\: \\ $$$${impossible}…
Question Number 46401 by Tawa1 last updated on 25/Oct/18 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}:\:\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\sqrt{\mathrm{x}}}\:,\:\:\frac{\mathrm{1}}{\mathrm{1}\:−\:\mathrm{x}}\:,\:\:\frac{\mathrm{1}}{\mathrm{1}\:−\:\sqrt{\mathrm{x}}}\:\:,\:\:…\: \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 25/Oct/18 $${pls}\:{add}\:{few}\:{more}\:{term}\:{or}\:{upload}\:{the}\:{photo}\:{of}\:{question}… \\ $$ Terms of Service…
Question Number 46395 by Meritguide1234 last updated on 25/Oct/18 Answered by MJS last updated on 25/Oct/18 $${x}=\sqrt{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{{x}}}}}}} \\ $$$${x}=\sqrt{\mathrm{5}}−\frac{\mathrm{5}{x}+\mathrm{3}}{\mathrm{8}{x}+\mathrm{5}} \\ $$$${x}^{\mathrm{2}} +\frac{\mathrm{5}−\mathrm{4}\sqrt{\mathrm{5}}}{\mathrm{4}}{x}+\frac{\mathrm{3}−\mathrm{5}\sqrt{\mathrm{5}}}{\mathrm{8}}=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =−\frac{\mathrm{7}}{\mathrm{4}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}}…
Question Number 111909 by john santu last updated on 05/Sep/20 $${solve}\:\begin{cases}{{x}\sqrt{{x}}+{y}\sqrt{{y}}\:=\:\mathrm{5}}\\{{x}\sqrt{{y}}\:+{y}\sqrt{{x}}\:=\:\mathrm{1}}\end{cases} \\ $$ Answered by bemath last updated on 05/Sep/20 $${let}\:\sqrt{{x}}\:=\:{u}\:;\:\sqrt{{y}}\:=\:{v} \\ $$$$\begin{cases}{{u}^{\mathrm{3}} +{v}^{\mathrm{3}} \:=\:\mathrm{5}\Rightarrow\left({u}+{v}\right)^{\mathrm{3}}…
Question Number 177442 by peter frank last updated on 05/Oct/22 Answered by mr W last updated on 05/Oct/22 $${x}\neq\mathrm{1} \\ $$$$\left({x}−\mathrm{1}\right)\left(\mathrm{1}+{x}+…+{x}^{\mathrm{2013}} \right)=\mathrm{0} \\ $$$${x}^{\mathrm{2014}} −\mathrm{1}=\mathrm{0}…
Question Number 46355 by denil last updated on 24/Oct/18 $${y}/{ax}−{b}={j} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 46348 by Saorey last updated on 24/Oct/18 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 177375 by a.lgnaoui last updated on 04/Oct/22 $$\mathrm{soit}\:\mathrm{k}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}\:,\mathrm{S}\:\mathrm{un}\:\mathrm{nombre}\:\mathrm{fini}\:\mathrm{de}\: \\ $$$$\mathrm{nombres}\:\mathrm{premiers}\:\mathrm{impair} \\ $$$$−\mathrm{Demontrer}\:\mathrm{qu}\:\mathrm{il}\:\mathrm{existe}\:\mathrm{au}\:\mathrm{plus}\:\mathrm{une}\:\mathrm{maniere}\left(\mathrm{a}\:\mathrm{rotation}\:\mathrm{et}\:\mathrm{symetrie}\:\mathrm{axiale}\right) \\ $$$$\mathrm{de}\:\mathrm{disposer}\:\mathrm{les}\:\mathrm{elements}\:\mathrm{de}\:\mathrm{S}\:\mathrm{sur}\:\mathrm{un}\:\mathrm{cercle}\:\mathrm{de}\:\mathrm{sorte}\:\mathrm{que}\:\mathrm{le}\:\mathrm{priduit}\:\mathrm{de}\:\mathrm{2}\:\mathrm{nombres}\: \\ $$$$\mathrm{places}\:\mathrm{l}'\mathrm{un}\:\mathrm{a}\:\mathrm{cote}\:\mathrm{de}\:\mathrm{l}'\mathrm{autre}\:\mathrm{soit}\:\mathrm{toujours}\:\mathrm{de}\:\mathrm{la}\:\mathrm{forme}\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{k}}\right),\mathrm{x}\:\mathrm{un}\:\mathrm{entier}\:\mathrm{naturel}\:\mathrm{non}\:\mathrm{nul}. \\ $$$$\:\:\:\:\:\:\:{Extrait}\:{de}\:{Olimpiad}\:{de}\:{Mathematiques}\:\left({France}\:\mathrm{2022}\right). \\ $$$$ \\ $$…